The Ibrox club forced Hearts into a difficult situation after making a move for John Souttar with the centre-back agreeing to join the cinch Premiership leaders in the summer.
Rangers have had a bid of £300,000 turned down for the 25-year-old, who sat out Saturday’s 5-0 victory over Auchinleck Talbot with an ankle knock.
Souttar’s decision to swap Gorgie for Govan on a potential free transfer, having been nursed back to health by Hearts throughout his various injury issues, has drawn ire from the Tynecastle support, with sections booing his every touch during the recent 2-0 win over St Johnstone.
It now seems Rangers could be set for a taste of their own medicine with the Scottish Sun reporting Nottingham Forest and West Bromich Albion are battling it out over Goldson with a pre-contract looking the most likely scenario.
The 29-year-old, who was an integral part of the improvement in the club under the guidance of former boss Steven Gerrard, still hasn’t ruled out signing an extension with the reigning champions.
Meanwhile, Hearts boss Robbie Neilson insists John Souttar will be in the squad for Wednesday’s home clash against Celtic unless Rangers make a satisfactory offer to sign him permanently in January before then.
He told Sky Sports: "John will train today so I expect him to be fully fit for Wednesday and I don't see anything changing until then.
"It's no problem at all, things will be bubbling away in the background. Whether another offer comes in or not I don't know, we'll wait and see. But at this moment John is a key player for us and he's giving 100 per cent every day in training. When he's been asked to play he's given 100 per cent as well, so I don't see that changing.
"I think all we have to do is just take it day by day. We've got a game on Wednesday, we'll prep for that and make sure John's part of the group for that.
"Then we'll see what today brings, what tomorrow brings."